Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92160 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, Sylow | #6861 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4179 |
| commutator, cosocle, hypocenter | C32⋊C9 | C2×C3 |
| Frattini | C33 | C3×D3 |
| Fitting | #6861 | C2 |
| socle | C32 | (C3⋊D3)⋊C3 |
| prime radical | #4181 | C3 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C3 | |
35 conjugacy classes of subgroups.
| minimal degree | μ(G) = 54 |
| transitive degree | μt(G) = 54 |
A minimal faithful permutation representation — 2 generators on 54 points:
(1,22,30,10,14,20,5,7,31,2,13,46,6,27,11,9,3,41)(4,32,49,36,34,51,19,35,29,15,12,54,18,45,37,25,16,47)(8,38,53,17,43,52,28,44,42,23,21,50,26,33,40,39,24,48);(1,18,23,6,19,17,5,4,39)(2,28,15,9,26,25,10,8,36)(3,34,38,13,16,33,14,12,44)(7,24,32,27,43,35,22,21,45)(11,49,52,31,37,48,30,29,50)(20,53,47,46,42,51,41,40,54)Polycyclic presentation:
2,3^5|b^3=f,c^3=e^2,c^a=c^2e,d^a=d^2f^2,e^a=e^2,c^b=cd,d^b=de,d^c=df^231 conjugacy classes — view the full character table.
| maximal subgroup of | #92165⋊C2, C2×#92166, C3×#92166, … |
| maximal normal subgroup of | #92165⋊C2, C2×#92166, C3×#92166, … |
| maximal quotient of | #11757289, C2×#92166, #13090452, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 11);